Defect inspection method and apparatus using micro lens matrix

ABSTRACT

A substrate surface defect detection device includes an optical waveguide for receiving first light and directing the received first light to a surface of a to be tested substrate, the optical waveguide having a first surface facing toward the substrate and a second surface facing away from the substrate, a microlens array disposed on the second surface of the optical waveguide, the microlens array including a plurality of microlenses arranged in an array for receiving second light from the surface of the to be tested substrate and converging the received second light to converged light, and an imaging component for receiving the converged light from the at least one microlens array for optical imaging. The substrate surface defect detection device requires significantly less time than conventional substrate surface defect detection devices.

CROSS-REFERENCES TO RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 15/706,409, filed Sep. 15, 2017, which claims priority toChinese Patent Application No. 201610826112.1, filed on Sep. 18, 2016,the contents of which are incorporated herein by reference in theirentirety.

FIELD OF THE INVENTION

The present disclosure relates to semiconductor technology. Moreparticularly, embodiments of the present disclosure relate to asubstrate surface defect detection apparatus and method, an imagedistortion correction method and apparatus, and a system including asubstrate surface defect detection apparatus and an image distortioncorrection apparatus.

BACKGROUND OF THE INVENTION

FIG. 1A is a perspective view of a conventional substrate surface defectdetection system 102. FIG. 1B is a plan view of a substrate 101 shown inFIG. 1A. As known in the art, the surface defects of a substrate 101need to be detected using a sophisticated and complex optical system102. FIG. 1B schematically shows the exposure area of substrate 101 andthe effective field of view of substrate surface defect detection system102. The effective field of view of substrate surface defect detectionsystem 102 is typically about 30 μm×30 μm. If system 102 is used todetect surface defects of substrate 101 having a typical exposure areaof 26 mm×33 mm, about one million operations must be performed tocomplete the surface defects detection (e.g., each shot only takes afield of view picture). If the time required to take a picture plus thetime required to move the detection system between the different shotstakes 0.5 second, it will take 50 million seconds, i.e., about 139 hoursto take pictures of the entire exposure area. It can be seen that theefficiency of current substrate surface defect detection systems andmethods is low.

BRIEF SUMMARY OF THE INVENTION

In accordance with the present disclosure, a novel substrate surfacedefect detection apparatus is provided that can significantly improvethe detection speed of substrate surface defects.

Embodiments of the present disclosure also provide an image distortioncorrection method and apparatus that are capable of correctingdistortion of an image output from a substrate surface defect detectionapparatus.

Embodiments of the present disclosure also provide substrate surfacedefect detection and image correction system.

Embodiments of the present disclosure also provide an apparatus andmethod for efficiently detecting substrate surface defects that canreduce the cost of defect detection.

In accordance to the present disclosure, a substrate surface defectdetection device may include an optical waveguide for receiving firstlight and directing the received first light to a surface of a to betested substrate, the optical waveguide having a first surface facingtoward the substrate and a second surface facing away from thesubstrate; at least one microlens array disposed on the second surfaceof the optical waveguide, the at least one microlens array comprising aplurality of microlenses arranged in an array for receiving second lightfrom the surface of the to be tested substrate and converging thereceived second light to converged light; and an imaging component forreceiving the converged light from the at least one microlens array forimaging.

In one embodiment, the imaging component includes a plurality of imagingunits, each of the imaging units comprising a plurality of pixels, eachof the imaging units being associated with one of the microlenses toreceive a portion of the converged light.

In one embodiment, the at least one microlens array includes a firstmicrolens array and a second microlens array stacked over each other.Each of the first and second microlens arrays has a plurality ofmicrolenses, each of the microlenses of the first microlens array has anoptical axis aligned to an optical axis of one corresponding microlensof the second microlens array.

In one embodiment, the substrate surface defect detection device mayfurther include a plurality of light confinement members disposedbetween a corresponding imaging unit and a corresponding microlens andconfigured to enable light from the corresponding microlens to reflect aspecific field of view to pass therethrough and into the correspondingimaging unit.

In one embodiment, the light confinement members each comprise a lightblocking plate. In one embodiment, the light confinement members eachinclude a cylindrical optical member having a light receiving surfaceand a light exit surface.

In one embodiment, the at least one microlens array further comprises asupport member disposed at an edge of the microlenses. In oneembodiment, the at least one microlens array includes a first microlensarray and a second microlens array stacked over each other, and thesupport member of the first microlens array and the support member ofthe second microlens array are aligned with each other.

In one embodiment, the support member is formed of a same material as amaterial of the microlenses and includes a barrier layer on a lowersurface for blocking light from entering the support member. In oneembodiment, the barrier layer includes a metal plating layer.

In one embodiment, the support member is formed of a same material as amaterial of the microlenses, and a surface portion of the opticalwaveguide below the support member includes a barrier layer for blockinglight from entering the support member.

In one embodiment, each of the microlenses includes a plano-convex lens.The coordinates of a point on an aspheric surface of the plano-convexlens in a z-direction parallel to an optical axis has a second orderfunction term and a fourth order function term of a distance from acorresponding plane projection point perpendicular to the optical axis.

In one embodiment, the aspheric surface of the plano-convex lens iscalculated by the following expression:

$Z = {\frac{\frac{1}{R}r^{2}}{1 + \sqrt{1 - {( {1 + K} )\frac{r^{2}}{R^{2\;}}}}} + {\alpha_{1}r^{2}} + {\alpha_{2}r^{4}}}$where r is a distance from a point of the aspheric surface perpendicularto the optical axis, Z is the coordinate of the point on the asphericsurface of the lens in the Z-direction, R is the radius of curvaturefrom the optical axis to the lens surface, K is a conic constant, α1 isan aspheric surface coefficient of the second order function term, andα2 is an aspheric surface coefficient of the fourth order function term.

In one embodiment, the optical waveguide includes a first incidentsurface and a second incident surface disposed on opposite sides of theoptical waveguide; the first light includes third light and fourthlight, the third light entering the optical waveguide from the firstincident surface and the fourth light entering the optical waveguidefrom the second incident surface.

In one embodiment, the first incident surface and the second incidentsurface are inclined with respect to the first surface of the opticalwaveguide.

In one embodiment, the substrate surface defect detection device mayfurther include a laser light source for generating a laser beam; asemitransparent mirror disposed at an angle relative to an optical axisof the laser beam for splitting the laser beam into first partial lightand second partial light; and a first light generating member forgenerating a first beam and including a first beam expander forexpanding the first partial light in a first dimension to generate afirst laser beam, a first lens for converging the first laser beam in asecond dimension different from the first dimension to generate aconverged first laser beam, and a first mirror for reflecting theconverged first laser beam as the third light entering the opticalwaveguide from the first incident surface.

In one embodiment, the substrate surface defect detection device mayfurther include a second mirror for reflecting the second partial light,and a second light generating member for generating a second beam thatincludes a second beam expander for expanding the second partial lightin the first dimension to generate a second laser beam, a second lensfor converging the second laser beam in the second dimension to generatea converged second laser beam, and a third mirror for reflecting theconverged second laser beam as the fourth light entering the opticalwaveguide from the second incident surface.

In one embodiment, the third light and the fourth light have a samelight intensity.

In one embodiment, the substrate surface defect detection device mayfurther include a spacer disposed on a side of the at least onemicrolens array and configured to block ambient light from entering themicrolenses.

In one embodiment, a sum of a thickness of the optical waveguide, athickness of the at least one microlens array, and an air gap betweenthe optical waveguide and the at least one microlens array is less thanor equal to 20 μm.

In one embodiment, an air gap between the surface of the to be testedsubstrate and the light receiving surface of the cylindrical opticalmember is less than or equal to 20 μm.

In one embodiment, each of the microlenses has a diameter in a rangebetween 5 μm and 20 μm.

In one embodiment, the optical waveguide includes a plurality ofscattering elements configured to scatter light transmitted by theoptical waveguide onto the surface of the to be tested substrate.

In one embodiment, the at least one microlens array further includes aplurality of support members disposed at an edge of the microlenses andconfigured to support corresponding microlenses disposed thereon. Eachof the plurality of scattering elements is disposed at a location of acorresponding one of the plurality of support members.

In one embodiment, the substrate is one of a semiconductor wafer, asemiconductor substrate, and a display panel. In one embodiment, theoptical waveguide, the at least one microlens array, and the imagingcomponent are configured such that a spot from light of a desiredimaging portion of the surface of the to be tested substrate incident onan imaging plane of the imaging component through the optical waveguideand the at least one microlens array is smaller than a size of an Airydisk.

Embodiments of the present disclosure also provide a method forcorrecting image distortion. The image distortion correcting method mayinclude obtaining a first light intensity of each pixel in an imagecomprising a plurality of pixels, the plurality of pixels including acenter pixel at the center or in a vicinity of the center of the imageand a first pixel different from the center pixel, calculating a firstdistance between the first pixel and the center pixel, calculating asecond distance between a second pixel and the center pixel, the secondpixel comprising at least a portion of pixels adjacent to the firstpixels, and correcting a light intensity of the first pixel based on thefirst light intensity of the first pixel, the first distance, the seconddistance, and the first light intensity of the second pixel.

In one embodiment, the first pixel has coordinates (i, j), the centerpixel has coordinates (0, 0), and the light intensity of the first pixelis corrected according to the following expression:P _((i,j)) =C ₁ P _((i,j)) +C ₂ P _((i−1,j−1)) +C ₃ P _((i−1,j)) +C ₄ P_((i,j−1))where i, j are non-zero integers, C1, C2, C3, C4 are the correctioncoefficients and C1+C2+C3+C4=1, is the light intensity of the firstpixel (i, j), and is the corrected light intensity of the pixel (i, j),and a pixel (i−1, j−1), a pixel (i−1, j), and a pixel (i, j−1) arepixels that are closer to the center pixel (0, 0) than the first pixel(i, j).

In one embodiment, the first pixel has coordinates (i, j), the centerpixel has coordinates (0, 0), and the light intensity of the first pixelis corrected according to the following expression:P _((i,j)) =C ₁ P _((i,j)) +C ₂ P _((i−1,j−1)) +C ₃ P _((i−1,j)) +C ₄ P_((i,j−1))where i, j are non-zero integers, C1, C2, C3, C4 are the correctioncoefficients and C1+C2+C3+C4=1, is the light intensity of the firstpixel (i, j), and is the corrected light intensity of the pixel (i, j),and a pixel (i+1, j+1), a pixel (i+1, j), and a pixel (i, j+1) arepixels that are father away from the center pixel (0, 0) than the firstpixel (i, j).

Embodiments of the present disclosure further provide an apparatus forcorrecting image distortion. The apparatus may include an obtaining unitconfigured to obtain a first light intensity of each pixel in an imagecomprising a plurality of pixels, the plurality of pixels including acenter pixel at the center or in a vicinity of the center of the imageand a first pixel different from the center pixel, a first calculationunit configured to calculate a first distance between the first pixeland the center pixel, a second calculation unit configured to calculatea second distance between a second pixel and the center pixel, thesecond pixel comprising at least a portion of pixels adjacent to thefirst pixels, and a correction unit configured to correct a lightintensity of the first pixel based on the first light intensity of thefirst pixel, the first distance, the second distance, and the firstlight intensity of the second pixel.

Embodiments of the present disclosure may also provide an apparatus thatincludes both the substrate surface defect detection device and theimage distortion correcting device described above.

The following description, together with the accompanying drawings, willprovide a better understanding of the nature and advantages of theclaimed disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the invention and are incorporated in and constitute apart of this application, illustrate certain embodiments of theinvention. In the drawings:

FIG. 1A is a perspective view of an optical system for substrate surfacedefects detection according to the prior art;

FIG. 1B is a plan view illustrating a substrate and the field of view ofthe optical system shown in FIG. 1A;

FIG. 2A is a schematic cross-sectional view of a substrate surfacedefect detection apparatus according to an embodiment of the presentdisclosure;

FIG. 2B is a perspective view illustrating the positional relationshipbetween the microlens array and the substrate surface according to anembodiment of the present disclosure;

FIG. 3 is a schematic cross-sectional view of a substrate surface defectdetection apparatus according to an embodiment of the presentdisclosure;

FIG. 4 is a perspective view illustrating a side illumination of themicrolens array from an optical waveguide according to an embodiment ofthe present disclosure;

FIG. 5 is a schematic cross-sectional view of a substrate surface defectdetection apparatus according to an embodiment of the presentdisclosure;

FIG. 6 is a schematic cross-sectional view of a structure of a substratesurface defect detection apparatus according to an embodiment of thepresent disclosure;

FIG. 7 is a simplified flowchart of a method for image distortioncorrection according to an embodiment of the present disclosure;

FIG. 8A is a schematic view of a barrel-shaped distortion according toan embodiment of the present disclosure;

FIG. 8B is a schematic view of a pillow-shaped distortion according toan embodiment of the present disclosure;

FIG. 9A shows a correction of a first pixel according to an embodimentof the present disclosure;

FIG. 9B shows a correction of a first pixel according to an embodimentof the present disclosure

FIG. 10 is a simplified block diagram of a image distortion correctionapparatus according to an embodiment of the present disclosure; and

FIG. 11 is a simplified block diagram of a computing apparatus that maybe programmed to execute codes for correcting image distortion accordingto one embodiment of the present disclosure.

DETAILED DESCRIPTION OF THE INVENTION

In the following description, numerous specific details are provided fora thorough understanding of the present invention. However, it should beappreciated by those of skill in the art that the present invention maybe realized without one or more of these details. In other examples,features and techniques known in the art will not be described forpurposes of brevity.

It should be understood that the drawings are not drawn to scale, andsimilar reference numbers are used for representing similar elements.Embodiments of the invention are described herein with reference tocross-section illustrations that are schematic illustrations ofidealized embodiments (and intermediate structures) of the invention.The thickness of layers and regions in the drawings may be exaggeratedrelative to each other for clarity. Additionally, variations from theshapes of the illustrations as a result, for example, of manufacturingtechniques and/or tolerances, are to be expected. Thus, embodiments ofthe disclosure should not be construed as limited to the particularshapes of regions illustrated herein but are to include deviations inshapes that result, for example, from manufacturing.

It will be understood that, when an element or layer is referred to as“on,” “disposed on,” “adjacent to,” “connected to,” or “coupled to”another element or layer, it can be disposed directly on the otherelement or layer, adjacent to, connected or coupled to the other elementor layer, or intervening elements or layers may also be present. Incontrast, when an element is referred to as being “directly on,”directly disposed on,” “directly connected to,” or “directly coupled to”another element or layer, there are no intervening elements or layerspresent between them. It will be understood that, although the terms“first,” “second,” “third,” etc. may be used herein to describe variouselements, components, regions, layers and/or sections, these elements,components, regions, layers and/or sections should not be limited bythese terms. These terms are only used to distinguish one element,component, region, layer or section from another region, layer orsection. Thus, a first element, component, region, layer or sectiondiscussed below could be termed a second element, component, region,layer or section without departing from the teachings of the presentdisclosure.

Relative terms such as “under,” “below,” “underneath,” “over,” “on,”“above,” “bottom,” and “top” are used herein to described a relationshipof one element, layer or region to another element, layer or region asillustrated in the figures. It will be understood that these terms areintended to encompass different orientations of the structure inaddition to the orientation depicted in the figures. For example, if thedevice shown in the figures is flipped, the description of an elementbeing “below” or “underneath” another element would then be oriented as“above” the other element. Therefore, the term “below,” “under,” or“underneath” can encompass both orientations of the device. Becausedevices or components of embodiments of the present disclosure can bepositioned in a number of different orientations (e.g., rotated 90degrees or at other orientations), the relative terms should beinterpreted accordingly.

The terms “a”, “an” and “the” may include singular and pluralreferences. It will be further understood that the terms “comprising”,“including”, having” and variants thereof, when used in thisspecification, specify the presence of stated features, steps,operations, elements, and/or components, but do not preclude thepresence or addition of one or more other features, steps, operations,elements, components, and/or groups thereof. Furthermore, as usedherein, the words “and/or” may refer to and encompass any possiblecombinations of one or more of the associated listed items.

The use of the terms first, second, etc. do not denote any order, butrather the terms first, second, etc. are used to distinguish one elementfrom another. Furthermore, the use of the terms a, an, etc. does notdenote a limitation of quantity, but rather denote the presence of atleast one of the referenced items.

The term “vertical” as used in this application is defined as a planeperpendicular to the conventional plane or surface of a wafer orsubstrate, regardless of the orientation of the wafer or substrate. Theterm “horizontal” refers to a direction perpendicular to the vertical asdefined above.

It should be noted that similar parts are given reference numerals andsymbols as similar as possible throughout the drawings. Once a part hasbeen defined and described, it will not be described again in subsequentdrawings.

In the present disclosure, a substrate may include one or more wafersselected from a group consisting of a semiconductor wafer, asemiconductor substrate, and a display panel.

The present disclosure will be described by way of illustratingembodiments with reference to the accompanying drawings.

FIG. 2A is a schematic cross-sectional view of a substrate surfacedefect detection device according to an embodiment of the presentdisclosure. As shown in FIG. 2A, the substrate surface defect detectiondevice may include an optical waveguide 201, at least one microlensarray 202, and an imaging component 203. The substrate surface defectdetection device will be described in detail below.

Optical waveguide 201 is configured to receive light and direct light tothe surface of a to be tested substrate 101. Optical waveguide 201 has afirst surface adjacent to (facing toward) substrate 101 and a secondsurface opposite the first surface (i.e., facing away from thesubstrate). Microlens array 202 is arranged on the side of opticalwaveguide 201 opposite substrate 101, i.e., microlens 202 is disposed onthe side where the second surface of optical waveguide 201 is located.Imaging component 203 is configured to receive light from the microlensarray for imaging.

In one embodiment, optical waveguide 201 may include a plurality ofscattering elements 2011 configured to scatter the light transmitted inoptical waveguide 201 onto the surface of the to be tested substrate101. The scattering elements 2011 may be obtained by ion bombardment ofoptical waveguide 201, or by laser focusing to local portions of opticalwaveguide 201 in such a manner that the local portions of opticalwaveguide 201 are melted.

In one embodiment, microlens array 202 may be glued together withoptical waveguide 201. The at least one microlens array 202 may includea first microlens array 212 and a second microlens array 222 stacked ontop of each other, as shown in FIG. 2A. In one embodiment, the at leastone microlens array 202 may be configured such that the optical axis ofthe microlenses in one microlens array is aligned with the optical axisof the corresponding microlenses in another microlens array (asindicated by the dotted lines shown in FIG. 2A). Each microlens arrayincludes a plurality of microlenses arranged in an array for receivingand converging light from the surface of the to be tested substratepassing through optical waveguide 201. In one embodiment, the diameterof a microlens may be in the range between 5 μm and 20 μm, e.g., 10 μm.

It is to be understood that microlens array 202 may include multiplemicrolens arrays, such as a third microlens array (not shown) disposedon second microlens array 222, and adjacent microlens arrays may beglued together. In one embodiment, the microlens array may also includea support member (e.g., a cylindrical member) disposed at the peripheraledge of the microlens that can be used to support a microlens adjacentthereto. In one embodiment, the support member (shown as a protrusionhaving a rectangular shape in FIG. 2A) of first microlens array 212 andthe support member of second microlens array 222 are aligned with eachother, as shown in FIG. 2A. In the case where optical waveguide 201includes a plurality of scattering elements 2011, the scatteringelements may be provided as to correspond to the respective supportmembers of the microlens array. For example, scattering member 2011 maybe provided at a location of optical waveguide 201 below a correspondingsupport member of a microlens array.

In one embodiment, imaging component 203 may include a plurality ofimaging units. Imaging component 203 may include a first imaging unit213, a second imaging unit 223, a third imaging unit 233, as shown inFIG. 2A. Each imaging unit may include a plurality of pixels. Eachimaging unit corresponds to a microlens to receive at least a portion ofthe light passing through the microlens for forming an image.

In one embodiment, optical waveguide 201, microlens array 202, andimaging component 203 shown in FIG. 2A may be configured such that aspot formed by light transmitting from the desired imaging portion ofthe surface of the to be tested substrate and passing through opticalwaveguide 201 and microlens array 202 and incident on the imaging planeof imaging component 203 satisfies the diffraction limit requirement,i.e., the spot is less than the size of the Airy disk. In oneembodiment, the sum of the thickness of optical waveguide 201, thethickness of microlens array 202, and the spacing (air gap) betweenoptical waveguide 201 and microlens array 202 is less than or equal to20 μm. In a specific embodiment, the thickness of optical waveguide 201,the thickness of microlens array 202, and the air gap between opticalwaveguide 201 and microlens array 202 each are less than or equal to 10μm.

As will be described in more detail below, the substrate surface defectdetection device provided by the present disclosure can detect a surfacedefect of the substrate by the imaging of the microlens array. Since themicrolens array includes a plurality of microlenses, the image of thesubstrate surface at different locations of the substrate can beobtained by moving the substrate only one time, so that the detectionspeed of the surface defects of the substrate can be increased.

In practical applications, the substrate surface defect detection speedcan be improved multiple times by setting the size of the microlensarray, the diameter of the microlens, and the field of view of themicrolens. For example, in the case where the diameter of the microlensis 10 μm, the size of the microlens can be set to be the same as theexposure area, as shown in FIG. 2B. In the case where any imaging pointof the microlens in the field of view of 1 μm×1 μm satisfies thediffraction limit, an exposure area can be completely scanned using 100pictures, the detection speed can be increased to 10,000 (ten thousands)times over the current techniques. In the case where any imaging pointof the microlens in the field of view of 2 μm×2 μm satisfies thediffraction limit, an exposure area can be completely scanned using 25pictures, the detection speed can be improved to 40,000 times over thecurrent techniques.

Of course, it will be appreciated that the size of the microlens arraymay also be set to be different from the exposure area, and it is stillpossible to increase the defect detection speed. For example, themicrolens array may be set to an array of 100×100 microlenses, or1000×1000 microlenses.

It is to be noted that the microlenses in the microlens array mayinclude, but are not limited to, a plano-convex lens element, a convexlens element, convex-concave (meniscus) lens element, etc., as long asthe microlens can converge light.

In practical applications, a plano-convex lens element is preferred tothe convenience of processing and assembling of the microlenses. Becausethe plano-convex lens element includes a plane, the use of theplano-convex microlenses makes the processing and assembling easier,thereby reducing the manufacturing cost of the microlens array.

FIG. 3 is a schematic view of a substrate surface defect detectiondevice according to another embodiment of the present disclosure. Asshown in FIG. 3, the substrate surface defect detection device mayfurther include a plurality of light confinement members 301 disposedbetween the corresponding imaging unit of the imaging component and themicrolens of the microlens array. Light confinement members 301 areconfigured to enable the light from the corresponding microlens toreflect a specific field of view to pass through and into thecorresponding imaging unit. In one embodiment, light confinement members301 each may include a cylindrical optical member 311 and a lightblocking plate 321. Cylindrical optical members 311 each include a lightreceiving surface and a light exit surface, and light from acorresponding microlens reflecting a specific field of view enterscylindrical optical member 311 through the light receiving surface andenters a corresponding image forming unit through the light exitsurface. In one embodiment, the distance between the surface of the tobe tested substrate 101 and the light receiving surface of the lightreceiving surface of cylindrical optical member 311 is less than orequal to 20 μm. Light blocking plate 321 may surround the peripheralsurface of cylindrical optical member 311 with the exception of thelight receiving surface and the light exit surface so that light fromthe corresponding microlens reflecting the specific field of view doesnot enter adjacent imaging units. It is to be understood that theabove-described specific field of view may be a field of view ofdifferent dimensions dependent on the optical waveguide and theparameters of the microlens, e.g., a field of view of 1 μm×1 μm, 2 μm×2μm, etc. However, in other embodiments, light confinement members 301each may include only light blocking member 321. As a non-limitingexemplary embodiment, light blocking member 321 may be metal,polysilicon, or carbon powder.

In one embodiment, optical waveguide 201, microlens array 202,cylindrical optical element 311, and imaging component 203 shown in FIG.3 may be configured such that a spot formed by light from the desiredimaging portion of the to be tested substrate 101 passes through opticalwaveguide 201, microlens array 202, and cylindrical optical element 311and incident to imaging component 203 satisfies the diffraction limitrequirement, i.e., the spot is less than the size of the Airy disk.

In the microlens array having the support member, the support member maybe formed of the same material as the microlens, for example, quartzglass. In this case, light transmitted in optical waveguide 201 mayenter the support member, thereby entering the microlens and affectingthe imaging quality of the microlens. In order to eliminate this effect,in one embodiment, the substrate surface defect detection device mayfurther include a barrier layer 302 disposed on the lower surface of thesupport member and/or on a portion of the second surface of opticalwaveguide 201 under the support member, as shown in FIG. 3. Barrierlayer 302 is configured to block light entering into the support member.Barrier layer 302 may include a metal plating layer.

Further, undesired light such as ambient light may also enter themicrolens through the side of the microlens array, thereby affecting theimaging quality of the microlens. In order to eliminate this effect, inone embodiment, the substrate surface defect detection device mayfurther include a spacer 303 disposed at the sides of microlens array202 for blocking ambient light from entering the microlenses, therebypreventing ambient light from affecting the imaging quality of themicrolenses, as shown in FIG. 3.

For a substrate surface defect detection device having a microlensarray, the distance between the microlenses and the substrate surface issmall, e.g., only a few microns (m), which presents a requirement forhigh radiance of illumination. The present disclosure provides thefollowing solution to the illumination problem of the substrate surfacedefect detection device.

FIG. 4 is a perspective view illustrating a side illumination of themicrolens array from an optical waveguide according to an embodiment ofthe present disclosure. Referring to FIG. 4, optical waveguide 201 mayinclude a first incident surface 211 and a second incident surface 221on opposite sides of the optical waveguide. Incident light on opticalwaveguide 201 may include a first incident light 401 and a secondincident light 402 entering optical waveguide 201 from respective firstincident surface 211 and second incident surface 221 of the opticalwaveguide. In one embodiment, the light intensity of first incidentlight 401 and second incident light 402 can be substantially the same,so that the uniformity of incident light on the surface of the to betested substrate is improved, and the uniformity of the incident lightreceived from the substrate surface to be measured by the microlenses isalso improved, so that the image distortion caused by the inhomogeneityof incident can be reduced. For example, first incident light 401 andsecond incident light 402 may be ultraviolet light. In one embodiment,first incident light 401 and second incident light 402 may beultraviolet light having a wave length of about 193 nm (e.g., 192.5 to193.5 nm). Of course, the present disclosure is not limited thereto.

In one embodiment, first incident surface 211 and second incidentsurface 221 are inclined with respect to the first surface of opticalwaveguide 201 so that the incident angles of first incident light 401and second incident light 402 can be more easily adjusted so that firstincident light 401 and second incident light 402 are transmitted in theoptical waveguide in a totally reflective manner. For example, theangles between first incident surface 211 and second incident surface221 and the first surface (i.e., the bottom surface of optical waveguide201) each can be an acute angle.

FIG. 5 is a schematic view of a substrate surface defect detectionapparatus according to an embodiment of the present disclosure.Referring to FIG. 5, the substrate surface defect detection device mayfurther include a laser light source 501, a semitransparent mirror 502,and a first light generating member 503 for generating first light.Laser light source 501 is configured to generate a laser beam, e.g.,ultraviolet light having a wavelength of about 193 nm. Semitransparentmirror 502 is disposed at an angle relative to the optical axis of thelaser light source and configured to split the laser beam into firstpartial light (reflected light) 601 and second partial light(transmitted light) 602. First light generating member 503 includes afirst beam expander 513, a first lens 523, and a first mirror 533. Firstbeam expander 513 is configured to expand the first portion of the lightfrom semitransparent mirror 502 in the first dimension (in the dimensionperpendicular to the drawing plane as shown in FIG. 5) to generate afirst laser beam after the beam expansion. First lens 523 is configuredto converge the beam of the first laser beam after the beam expansion ina second dimension different from the first dimension (in the dimensionparallel to the drawing plane in the horizontal direction) to generatethe converged first laser beam after the beam convergence. First mirror533 is configured to reflect the converged first laser beam so as to beincident on the first incident surface of optical waveguide 201 as firstlight 401.

Referring still to FIG. 5, the substrate surface defect detection devicemay further include a second mirror 504 and a second light generatingmember 505 for generating second light. Second mirror 504 is configuredto reflect second partial light 602 from laser light source 501. Secondlight generating member 505 may include a second beam expander 515, asecond lens 525, and a third mirror 535. Second beam expander 515 isconfigured to expand the first portion of the light from semitransparentmirror 502 in the first dimension (e.g., in the dimension perpendicularto the drawing plane as shown in FIG. 5) to generate a second laser beamafter the beam expansion. Second lens 525 is configured to converge theexpanded second laser beam after the beam expansion in the seconddimension different from the first dimension (e.g., in the dimensionparallel to the drawing plane in the horizontal direction) to generatethe converged second laser beam after the beam convergence. Third mirror535 is configured to reflect the converged second laser beam so as to beincident on the second incident surface of optical waveguide 201 assecond light 402.

FIG. 6 is a schematic view of a structure of a substrate surface defectdetection apparatus according to an embodiment of the presentdisclosure. Referring to FIG. 6, the distance S1 between substrate 101and the first surface of optical waveguide 201 may be in the rangebetween 1 μm and 3 μm; the thickness S2 of optical waveguide 201 may beabout 2 μm; the distance S3 between the second surface of opticalwaveguide 201 and first microlens array 212 may be in the range between0.5 μm and 1 μm; the thickness S4 of first microlens array 212 may be inthe range between 1 μm and 6 μm; the distance S5 between first microlensarray 212 and second microlens array 222 may be in the range between 1μm and 5 μm; the thickness S6 of second microlens array 222 may be inthe range between 1 μm and 3 μm; the distance S7 between secondmicrolens array 222 and cylindrical optical member 311 may be in therange between 0.5 μm and 1.5 μm; cylindrical optical member 311 has alength S8 in the range between 30 μm and 120 μm; the distance S9 betweensecond cylindrical optical member 311 and imaging component 203 may bein the range between 0.5 μm and 1.5 μm.

The parameters of the components of the substrate surface defectdetection device are described below in two specific embodiments.

In the following embodiments, the microlens may be a plano-convex lens.In one embodiment, the coordinates of the Z-direction (parallel to theoptical axis) of a point on the aspheric surface of the convex lens maybe a second order function term to a fourth order function term of thedistance r of a corresponding plane projection point on the planeperpendicular to the optical axis. Further, the aspheric surface of theconvex lens can be expressed using the following expression:

$Z = {\frac{\frac{1}{R}r^{2}}{1 + \sqrt{1 - {( {1 + K} )\frac{r^{2}}{R^{2\;}}}}} + {\alpha_{1}r^{2}} + {\alpha_{2}r^{4}}}$where r is the distance from the point of the aspheric surfaceperpendicular to the optical axis, Z is the coordinate of the point onthe aspheric surface of the lens in the Z-direction (i.e., the height ofa point on the aspheric surface at a distance r from the optical axisrelative to the tangential plane at the aspheric surface vertex), R isthe radius of curvature from the optical axis to the lens surface, K isa conic constant, α1 is an aspheric surface coefficient of the secondorder term, and α2 is an aspheric surface coefficient of the fourthorder term. For a plano-convex lens, K is 0 (zero).

In one embodiment, the aspheric surface of the microlens of firstmicrolens array 212 can be expressed using the following expression:

$Z = {\frac{\frac{1}{5.503}r^{2}}{1 + \sqrt{1 - \frac{r^{2}}{5.503^{2}}}} - {128.604r^{2}} - {1.59 \times 10^{6}r^{4}}}$

the aspheric surface of the microlens of second microlens array 222 canbe expressed using the following expression:

$Z = {\frac{\frac{1}{- 1.206}r^{2}}{1 + \sqrt{1 - \frac{r^{2}}{( {- 1.206} )^{2}}}} - {97.857r^{2}} - {7.285 \times 10^{4}r^{4}}}$

In the embodiment, the diameter of first microlens array 212 and secondmicrolens array 222 may be set to 10 μm. The microlens array formed byfirst microlens array 212 and second microlens array 222 has a numericalaperture of 0.7 and a 9× magnification. In this case, the value of theparameters S1 through S9 may be set as follows: S1 is about 1.5 μm, S2is about 2 μm, S3 is about 0.5 μm, S4 is about 2 μm, S5 is about 1.3 μm,S6 is about 3 μm, S7 is about 1 μm, S8 is about 95 μm, and S9 is about 1μm. In the case where the filed of view is 1 μm×1 μm, a spot formed bylight from the desired imaged portion of the surface of the to be testedsubstrate 101 passing through optical waveguide 201, microlens array 202and cylindrical optical member 311 is incident on imaging member 203satisfies the diffraction limit requirement, i.e., the size (innercircle) of the actual spot is smaller than the size of the Airy disk(outer circle). At this point, the depth of focus can be extended to±0.31 μm, the maximum distortion is about 0.30%, about 3 nm. Theembodiment enables the defect detection speed to be 10,000 times fasterthan the defect detection speed of a conventional substrate surfacedefect detection device.

In another embodiment, the aspheric surface of the microlens of firstmicrolens array 212 can be expressed using the following expression:

$Z = {\frac{\frac{1}{9.995}r^{2}}{1 + \sqrt{1 - \frac{r^{2}}{9.995^{2}}}} - {29.93r^{2}}}$

the aspheric surface of the microlens of second microlens array 222 canbe expressed using the following expression:

$Z = {\frac{\frac{1}{28}r^{2}}{1 + \sqrt{1 - \frac{r^{2}}{28^{2}}}} - {43.969r^{2}}}$

In the embodiment, the diameter of first microlens array 212 and secondmicrolens array 222 may be set to 10 μm. The microlens array formed byfirst microlens array 212 and second microlens array 222 has a numericalaperture of 0.9 and a 5× magnification. In this case, the value of theparameters S1 through S9 may be set as follows: S1 is about 1.5 μm, S2is about 2 μm, S3 is about 0.5 μm, S4 is about 5 μm, S5 is about 4.5 μm,S6 is about 3 μm, S7 is about 1 μm, S8 is about 40 μm, and S9 is about 1μm. In the case where the filed of view is 2 μm×2 μm, a spot formed bylight from the desired imaged portion of the surface of the to be testedsubstrate 101 passing through optical waveguide 201, microlens array 202and cylindrical optical member 311 is incident on imaging member 203satisfies the diffraction limit requirement, i.e., the size (innercircle) of the actual spot is smaller than the size of the Airy disk(outer circle). At this point, the depth of focus can be extended to ±5μm. The embodiment enables the defect detection speed to be 40,000 timesfaster than the defect detection speed of a conventional substratesurface defect detection device.

It is to be understood that both embodiments described above are merelyexemplary and are not intended to limit the scope of the presentdisclosure. Those of skill in the art can adjust the parameters of thecomponents in the substrate surface defect detection device inaccordance with the teachings of the present disclosure so the spotsformed on the imaging plane of the imaging member in different field ofview satisfy the diffraction limit requirement so that the defectdetection speed can be improved by several orders of magnitude.

For a single microlens, the distortion of the image may be very small.However, image distortion may be severe when the cumulative effect ofthe microlenses is taken into consideration. Therefore, after imagingwith the above-described image forming member, the resulting image maybe deviated from the desired location due to the presence of distortion.In view of this problem, the present disclosure also provides a methodand apparatus for correcting image distortion that will be described indetail below.

FIG. 7 is a simplified flowchart of a method for image distortioncorrection according to an embodiment of the present disclosure. Themethod may include the following steps:

Step 702: obtaining a light intensity of each pixel in an imagecomprising a plurality of pixels, the plurality of pixels may include acenter pixel located in the center or near the center of the image and afirst pixel different from the center pixel.

The image comprising the plurality of pixels maybe an image formed byimaging unit 203 that receives light from the microlens array. Thecenter pixel may be in the center of the image, or in the vicinity ofthe center of the image, or defined by the user at a location of theimage.

Step 704: calculating (computing using a computer) a first distancebetween the first pixel and the center pixel.

Step 706: calculating a second distance between the center pixel and asecond pixel in at least a portion of the pixels adjacent to (in thevicinity of) the center pixel.

The portion of the pixels adjacent to the center pixel may include aplurality of pixels, and the second pixel may include a portion of theportion of the pixels adjacent to the center pixel, or the second pixelmay include the entire portion of the pixels adjacent to the centerpixel. In one embodiment, the second pixel is not the center pixel.

Step 708: correcting the light intensity of the first pixel based on thelight intensity of first pixel, the first distance, the second distance,and the light intensity of the second pixel.

The method for correcting an image distortion according to the presentdisclosure can correct the light intensity of the first pixel based onthe light intensity of the first pixel and the light intensity of atleast a portion of the second pixel adjacent to the first pixel, so thatthe obtained image can be made closed to the actual image.

In general, the distortion in the microlens imaging process may includetwo main types: one type is barrel distortion, as shown in FIG. 8A. Theother type is pin-cushion distortion, as shown in FIG. 8B. In FIGS. 8Aand 8B, the dotted lines represent the ideal image of the imaging unitwithout distortion. The four small boxes represent four adjacent pixels.For these two distortion types, the distortion correction can beimplemented in different ways and will be described in detail below.

In one embodiment, the light intensity of the first pixel may becorrected based on the light intensity of the first pixel and the lightintensity of the three pixels whose second distance is smaller than thefirst distance of the first pixel to the center pixel. Referring to FIG.9A, the coordinates of the first pixel are (i, j), the coordinates ofthe center pixel are (0, 0), the pixel (i−1, j−1), the pixel (i−1, j),and the pixel (i, j−1) are pixels that are closer to the center pixel(0, 0) than the first pixel (i, j). That is, the second distance of thethree pixels from the center pixel is smaller than the first distance ofthe first pixel (i, j) from the center pixel (0, 0). Specifically, thelight intensity of the first pixel can be corrected using the followingexpression:P _((i,j)) =C ₁ P _((i,j)) +C ₂ P _((i−1,j−1)) +C ₃ P _((i−1,j)) +C ₄ P_((i,j−1))where i, j are non-zero integers, C1, C2, C3, C4 are the correctioncoefficients and C1+C2+C3+C4=1, P_((i,j)) is the light intensity of thefirst pixel (i, j), and P_((i,j)) is the corrected light intensity ofthe pixel (i, j).

This correction method is suitable for the image having the barreldistortion as shown in FIG. 8A. The light intensity of the first pixelcan be corrected using the original light intensity of the first pixeland the light intensity of the three adjacent pixels closer to thecenter pixel than the first pixel so that the image having the barreldistortion can be corrected.

In another embodiment, the light intensity of the first pixel may becorrected based on the light intensity of the first pixel and the lightintensity of the three pixels whose second distance is greater than thefirst distance of the first pixel to the center pixel. Referring to FIG.9B, the coordinates of the first pixel are (i, j), the coordinates ofthe center pixel are (0, 0), the pixel (i+1, j+1), the pixel (i+1, j),and the pixel (i, j+1) are pixels that are farther away from the centerpixel (0, 0) than the first pixel (i, j). That is, the second distanceof the three pixels from the center pixel is greater than the firstdistance of the first pixel (i, j) from the center pixel (0, 0).Specifically, the light intensity of the first pixel can be correctedusing the following expression:P _((i,j)) =C ₁ P _((i,j)) +C ₂ P _((i+1,j+1)) +C ₃ P _((i+1,j)) +C ₄ P_((i,j+1))where i, j are non-zero integers, C1, C2, C3, C4 are the correctioncoefficients and C1+C2+C3+C4=1, P_((i,j)) is the light intensity of thefirst pixel (i, j), and P_((i,j)) is the corrected light intensity ofthe pixel (i, j).

This correction method is suitable for the image having the pin-cushiondistortion as shown in FIG. 8B. The light intensity of the first pixelcan be corrected using the original light intensity of the first pixeland the light intensity of the three adjacent pixels that are fartheraway from the center pixel than the first pixel so that the image havingthe pin-cushion distortion can be corrected.

The present disclosure thus provides methods for correcting an imagehaving distortion. It can be assuming that the size and trend of thedistortion amount of each microlens are the same so that the processingefficiency of the image pattern can be improved.

The present disclosure also provides a correction device for correctingimage distortion.

FIG. 10 is a simplified block diagram of an image distortion correctiondevice according to an embodiment of the present disclosure. Referringto FIG. 10, the image distortion correction device include an obtainingunit 1001, a first calculation unit 1002, a second calculation unit1003, and a correction unit 1004. Obtaining unit 1001 is configured toobtain the light intensity of each pixel in an image including aplurality of pixels. The plurality of pixels may include a center pixeldisposed at the center or near the center of the image and a first pixeldifferent form the center pixel. First calculation unit 1002 isconfigured to calculate the first distance between the first pixel andthe center pixel. Second calculation unit 1003 is configured tocalculate a second distance between a second pixel and the first pixel,the second pixel may be at least a portion of the pixels adjacent to thefirst pixel. Correction unit 1004 is configured to correct the lightintensity of the first pixel based on the original light intensity ofthe first pixel, the first distance, the second distance and the lightintensity of the second pixel.

The image distortion correction device according to the presentinvention can correct the light intensity of the first pixel using theoriginally obtained light intensity of the first pixel and of the secondpixel that includes at least a portion of the pixels adjacent to thefirst pixel, so that the resulting image can be made closer to theactual image. In practical applications, the function of the imagedistortion correction device can be implemented by hardware (e.g.,circuit logic, FPGA, one or more processing units) or by software havingprogram code and instructions stored in a computer readable storagemedium.

For different distortion types, correction unit 1004 may correct thelight intensity of the first pixel using different approaches.

In one embodiment, the image may have a barrel distortion. Referring toFIG. 9A, the coordinates of the first pixel are (i, j), the coordinatesof the center pixel are (0, 0), the pixel (i−1, j−1), the pixel (i−1,j), and the pixel (i, j−1) are pixels that are closer to the centerpixel (0, 0) than the first pixel (i, j). That is, the second distanceof the three pixels from the center pixel is smaller than the firstdistance of the first pixel (i, j) from the center pixel (0, 0).Specifically, the light intensity of the first pixel can be correctedusing the following expression:P _((i,j)) =C ₁ P _((i,j)) +C ₂ P _((i−1,j−1)) +C ₃ P _((i−1,j)) +C ₄ P_((i,j−1))where i, j are non-zero integers, C1, C2, C3, C4 are the correctioncoefficients and C1+C2+C3+C4=1, P_((i,j)) is the light intensity of thefirst pixel (i, j), and P_((i,j)) is the corrected light intensity ofthe pixel (i, j).

In another embodiment, the image may have a pin-cushion distortion.Referring to FIG. 9B, the coordinates of the first pixel are (i, j), thecoordinates of the center pixel are (0, 0), the pixel (i+1, j+1), thepixel (i+1, j), and the pixel (i, j+1) are pixels that are farther awayfrom the center pixel (0, 0) than the first pixel (i, j). That is, thesecond distance of the three pixels from the center pixel is greaterthan the first distance of the first pixel (i, j) from the center pixel(0, 0). Specifically, the light intensity of the first pixel can becorrected using the following expression:P _((i,j)) =C ₁ P _((i,j)) +C ₂ P _((i+1,j+1)) +C ₃ P _((i+1,j)) +C ₄ P_((i,j+1))where i, j are non-zero integers, C1, C2, C3, C4 are the correctioncoefficients and C1+C2+C3+C4=1, P_((i,j)) is the light intensity of thefirst pixel (i, j), and P_((i,j)) is the corrected light intensity ofthe pixel (i, j).

The present disclosure also provides a substrate surface defectdetection device that may be any one of the above-described substratesurface defect detection devices and a device for correcting imagedistortion that may be one of the above-described image distortioncorrection devices.

FIG. 11 is a simplified block diagram of a computing apparatus 1100 thatmay be programmed to execute codes for correcting image distortionaccording to one embodiment of the present disclosure. As shown,computing apparatus 1100 includes a processor having one or moreprocessing units, a system memory, static storage units (hard drive), adisplay unit (LCD), an input device (keyboard, mouse, optical disc ormagnetic tape reader, and the like). Computer apparatus 1100 alsoincludes a network interface unit configured to connect the computingapparatus with other devices through a local area network, a wide areanetwork, or a wireless network. In an embodiment, the display unit hasone or more windows for displaying the obtained light intensity of eachpixel of an image, the image distortion and the corrected image. Theinput device is connected to a digital camera for obtaining the lightintensity of each pixel of an image. The processor is configured tocalculate or compute the first distance between the first pixel and thecenter pixel, the second distance between the center pixel and thesecond pixel, and correct the light intensity of the first pixel basedon the obtained light intensity of the first and second pixel, the firstdistance, and the second distance. The computing apparatus shown in FIG.11 may include instruction codes that are stored in the system memoryand executable by the processor to perform the above-described distancecalculation and distortion correction.

The terms “device” and “apparatus” are used interchangeably. The terms“computing” and “calculating” are used interchangeably.

References in the specification to “one embodiment”, “an embodiment”,“an example embodiment”, “some embodiments”, etc., indicate that theembodiment described may include a particular feature, structure, orcharacteristic, but every embodiment may not necessarily include theparticular feature, structure, or characteristic. Moreover, such phrasesare not necessarily referring to the same embodiment. Further, when aparticular feature, structure, or characteristic is described inconnection with an embodiment, it is submitted that it is within theknowledge of one skilled in the art to affect such feature, structure,or characteristic in connection with other embodiments whether or notexplicitly described.

While the present disclosure is described herein with reference toillustrative embodiments, this description is not intended to beconstrued in a limiting sense. Rather, the purpose of the illustrativeembodiments is to make the spirit of the present disclosure be betterunderstood by those skilled in the art. In order not to obscure thescope of the disclosure, many details of well-known processes andmanufacturing techniques are omitted. Various modifications of theillustrative embodiments as well as other embodiments will be apparentto those of skill in the art upon reference to the description. It istherefore intended that the appended claims encompass any suchmodifications.

Furthermore, some of the features of the preferred embodiments of thepresent disclosure could be used to advantage without the correspondinguse of other features. As such, the foregoing description should beconsidered as merely illustrative of the principles of the disclosure,and not in limitation thereof.

What is claimed is:
 1. A method for correcting image distortion,comprising: obtaining, by a camera, a first light intensity of eachpixel in an image comprising a plurality of pixels, the plurality ofpixels including a center pixel at the center or in a vicinity of thecenter of the image and a first pixel different from the center pixel;calculating, by a processor, a first distance between the first pixeland the center pixel; calculating, by the processor, a second distancebetween a second pixel and the center pixel, the second pixel comprisingat least a portion of pixels adjacent to the first pixels; andcorrecting, by the processor, a light intensity of the first pixel basedon the first light intensity of the first pixel, the first distance, thesecond distance, and the first light intensity of the second pixel.
 2. Amethod for correcting image distortion, comprising: obtaining , by acamera, a first light intensity of each pixel in an image comprising aplurality of pixels, the plurality of pixels including a center pixel atthe center or in a vicinity of the center of the image and a first pixeldifferent from the center pixel; calculating , by a processor, a firstdistance between the first pixel and the center pixel; calculating , bythe processor, a second distance between a second pixel and the centerpixel, the second pixel comprising at least a portion of pixels adjacentto the first pixels; and correcting , by the processor, a lightintensity of the first pixel based on the first light intensity of thefirst pixel, the first distance, the second distance, and the firstlight intensity of the second pixel, wherein the first pixel hascoordinates (i, j), the center pixel has coordinates (0, 0), and thelight intensity of the first pixel is corrected according to thefollowing expression:P _((i,j)) =C ₁ P _((i,j)) +C ₂ P _((i−1,j−1)) +C ₃ P _((i−1,j)) +C ₄ P_((i,j−1)) where i, j are non-zero integers, C1, C2, C3, C4 are thecorrection coefficients and C1+C2+C3+C4=1, P_((i,j)) is the lightintensity of the first pixel (i, j), and P_((i,j)) is the correctedlight intensity of the pixel (i, j), and a pixel (i−1, j−1), a pixel(i−1, j), and a pixel (i, j−1) are pixels that are closer to the centerpixel (0, 0) than the first pixel (i, j).
 3. The method of claim 1,wherein the first pixel has coordinates (i, j), the center pixel hascoordinates (0, 0), and the light intensity of the first pixel iscorrected according to the following expression:P _((i,j)) =C ₁ P _((i,j)) +C ₂ P _((i−1,j−1)) +C ₃ P _((i−1,j)) +C ₄ P_((i,j−1)) where i, j are non-zero integers, C1, C2, C3, C4 are thecorrection coefficients and C1+C2+C3+C4=1, P_((i,j)) is the lightintensity of the first pixel (i, j), and P_((i,j)) is the correctedlight intensity of the pixel (i, j), and a pixel (i+1, j+1), a pixel(i+1, j), and a pixel (i, j+1) are pixels that are father away from thecenter pixel (0, 0) than the first pixel (i, j).
 4. An apparatus forcorrecting image distortion, comprising: a memory storing instructions;and a processor coupled to the memory and, when executing theinstructions, configured to: obtain, by a camera, a first lightintensity of each pixel in an image comprising a plurality of pixels,the plurality of pixels including a center pixel at the center or in avicinity of the center of the image and a first pixel different from thecenter pixel; calculate a first distance between the first pixel and thecenter pixel; calculate a second distance between a second pixel and thecenter pixel, the second pixel comprising at least a portion of pixelsadjacent to the first pixels; and correct a light intensity of the firstpixel based on the first light intensity of the first pixel, the firstdistance, the second distance, and the first light intensity of thesecond pixel.
 5. The apparatus of claim 4, wherein the first pixel hascoordinates (i, j), the center pixel has coordinates (0, 0), and thelight intensity of the first pixel is corrected according to thefollowing expression:P _((i,j)) =C ₁ P _((i,j)) +C ₂ P _((i−1,j−1)) +C ₃ P _((i−1,j)) +C ₄ P_((i,j−1)) where i, j are non-zero integers, C1, C2, C3, C4 are thecorrection coefficients and C1+C2+C3+C4=1, P_((i,j)) is the lightintensity of the first pixel (i, j), and P_((i,j)) is the correctedlight intensity of the pixel (i, j), and a pixel (i−1, j−1), a pixel(i−1, j), and a pixel (i, j−1) are pixels that are closer to the centerpixel (0, 0) than the first pixel (i, j).
 6. The apparatus of claim 4,wherein the first pixel has coordinates (i, j), the center pixel hascoordinates (0, 0), and the light intensity of the first pixel iscorrected according to the following expression:P _((i,j)) =C ₁ P _((i,j)) +C ₂ P _((i−1,j−1)) +C ₃ P _((i−1,j)) +C ₄ P_((i,j−1)) where i, j are non-zero integers, C1, C2, C3, C4 are thecorrection coefficients and C1+C2+C3+C4=1, P_((i,j)) is the lightintensity of the first pixel (i, j), and P_((i,j)) is the correctedlight intensity of the pixel (i, j), and a pixel (i+1, j+1), a pixel(i+1, j), and a pixel (i, j+1) are pixels that are father away from thecenter pixel (0, 0) than the first pixel (i, j).